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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.stat.inference;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.distribution.ChiSquaredDistribution;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.MaxCountExceededException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.NotPositiveException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.exception.NotStrictlyPositiveException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.exception.NullArgumentException;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.exception.OutOfRangeException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.exception.ZeroException;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.exception.util.LocalizedFormats;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.util.MathArrays;<a name="line.29"></a>
<FONT color="green">030</FONT>    <a name="line.30"></a>
<FONT color="green">031</FONT>    /**<a name="line.31"></a>
<FONT color="green">032</FONT>     * Implements Chi-Square test statistics.<a name="line.32"></a>
<FONT color="green">033</FONT>     *<a name="line.33"></a>
<FONT color="green">034</FONT>     * &lt;p&gt;This implementation handles both known and unknown distributions.&lt;/p&gt;<a name="line.34"></a>
<FONT color="green">035</FONT>     *<a name="line.35"></a>
<FONT color="green">036</FONT>     * &lt;p&gt;Two samples tests can be used when the distribution is unknown &lt;i&gt;a priori&lt;/i&gt;<a name="line.36"></a>
<FONT color="green">037</FONT>     * but provided by one sample, or when the hypothesis under test is that the two<a name="line.37"></a>
<FONT color="green">038</FONT>     * samples come from the same underlying distribution.&lt;/p&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     *<a name="line.39"></a>
<FONT color="green">040</FONT>     * @version $Id: ChiSquareTest.java 1416643 2012-12-03 19:37:14Z tn $<a name="line.40"></a>
<FONT color="green">041</FONT>     */<a name="line.41"></a>
<FONT color="green">042</FONT>    public class ChiSquareTest {<a name="line.42"></a>
<FONT color="green">043</FONT>    <a name="line.43"></a>
<FONT color="green">044</FONT>        /**<a name="line.44"></a>
<FONT color="green">045</FONT>         * Construct a ChiSquareTest<a name="line.45"></a>
<FONT color="green">046</FONT>         */<a name="line.46"></a>
<FONT color="green">047</FONT>        public ChiSquareTest() {<a name="line.47"></a>
<FONT color="green">048</FONT>            super();<a name="line.48"></a>
<FONT color="green">049</FONT>        }<a name="line.49"></a>
<FONT color="green">050</FONT>    <a name="line.50"></a>
<FONT color="green">051</FONT>        /**<a name="line.51"></a>
<FONT color="green">052</FONT>         * Computes the &lt;a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"&gt;<a name="line.52"></a>
<FONT color="green">053</FONT>         * Chi-Square statistic&lt;/a&gt; comparing &lt;code&gt;observed&lt;/code&gt; and &lt;code&gt;expected&lt;/code&gt;<a name="line.53"></a>
<FONT color="green">054</FONT>         * frequency counts.<a name="line.54"></a>
<FONT color="green">055</FONT>         * &lt;p&gt;<a name="line.55"></a>
<FONT color="green">056</FONT>         * This statistic can be used to perform a Chi-Square test evaluating the null<a name="line.56"></a>
<FONT color="green">057</FONT>         * hypothesis that the observed counts follow the expected distribution.&lt;/p&gt;<a name="line.57"></a>
<FONT color="green">058</FONT>         * &lt;p&gt;<a name="line.58"></a>
<FONT color="green">059</FONT>         * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.59"></a>
<FONT color="green">060</FONT>         * &lt;li&gt;Expected counts must all be positive.<a name="line.60"></a>
<FONT color="green">061</FONT>         * &lt;/li&gt;<a name="line.61"></a>
<FONT color="green">062</FONT>         * &lt;li&gt;Observed counts must all be &amp;ge; 0.<a name="line.62"></a>
<FONT color="green">063</FONT>         * &lt;/li&gt;<a name="line.63"></a>
<FONT color="green">064</FONT>         * &lt;li&gt;The observed and expected arrays must have the same length and<a name="line.64"></a>
<FONT color="green">065</FONT>         * their common length must be at least 2.<a name="line.65"></a>
<FONT color="green">066</FONT>         * &lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;<a name="line.66"></a>
<FONT color="green">067</FONT>         * If any of the preconditions are not met, an<a name="line.67"></a>
<FONT color="green">068</FONT>         * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.68"></a>
<FONT color="green">069</FONT>         * &lt;p&gt;&lt;strong&gt;Note: &lt;/strong&gt;This implementation rescales the<a name="line.69"></a>
<FONT color="green">070</FONT>         * &lt;code&gt;expected&lt;/code&gt; array if necessary to ensure that the sum of the<a name="line.70"></a>
<FONT color="green">071</FONT>         * expected and observed counts are equal.&lt;/p&gt;<a name="line.71"></a>
<FONT color="green">072</FONT>         *<a name="line.72"></a>
<FONT color="green">073</FONT>         * @param observed array of observed frequency counts<a name="line.73"></a>
<FONT color="green">074</FONT>         * @param expected array of expected frequency counts<a name="line.74"></a>
<FONT color="green">075</FONT>         * @return chiSquare test statistic<a name="line.75"></a>
<FONT color="green">076</FONT>         * @throws NotPositiveException if &lt;code&gt;observed&lt;/code&gt; has negative entries<a name="line.76"></a>
<FONT color="green">077</FONT>         * @throws NotStrictlyPositiveException if &lt;code&gt;expected&lt;/code&gt; has entries that are<a name="line.77"></a>
<FONT color="green">078</FONT>         * not strictly positive<a name="line.78"></a>
<FONT color="green">079</FONT>         * @throws DimensionMismatchException if the arrays length is less than 2<a name="line.79"></a>
<FONT color="green">080</FONT>         */<a name="line.80"></a>
<FONT color="green">081</FONT>        public double chiSquare(final double[] expected, final long[] observed)<a name="line.81"></a>
<FONT color="green">082</FONT>            throws NotPositiveException, NotStrictlyPositiveException,<a name="line.82"></a>
<FONT color="green">083</FONT>            DimensionMismatchException {<a name="line.83"></a>
<FONT color="green">084</FONT>    <a name="line.84"></a>
<FONT color="green">085</FONT>            if (expected.length &lt; 2) {<a name="line.85"></a>
<FONT color="green">086</FONT>                throw new DimensionMismatchException(expected.length, 2);<a name="line.86"></a>
<FONT color="green">087</FONT>            }<a name="line.87"></a>
<FONT color="green">088</FONT>            if (expected.length != observed.length) {<a name="line.88"></a>
<FONT color="green">089</FONT>                throw new DimensionMismatchException(expected.length, observed.length);<a name="line.89"></a>
<FONT color="green">090</FONT>            }<a name="line.90"></a>
<FONT color="green">091</FONT>            MathArrays.checkPositive(expected);<a name="line.91"></a>
<FONT color="green">092</FONT>            MathArrays.checkNonNegative(observed);<a name="line.92"></a>
<FONT color="green">093</FONT>    <a name="line.93"></a>
<FONT color="green">094</FONT>            double sumExpected = 0d;<a name="line.94"></a>
<FONT color="green">095</FONT>            double sumObserved = 0d;<a name="line.95"></a>
<FONT color="green">096</FONT>            for (int i = 0; i &lt; observed.length; i++) {<a name="line.96"></a>
<FONT color="green">097</FONT>                sumExpected += expected[i];<a name="line.97"></a>
<FONT color="green">098</FONT>                sumObserved += observed[i];<a name="line.98"></a>
<FONT color="green">099</FONT>            }<a name="line.99"></a>
<FONT color="green">100</FONT>            double ratio = 1.0d;<a name="line.100"></a>
<FONT color="green">101</FONT>            boolean rescale = false;<a name="line.101"></a>
<FONT color="green">102</FONT>            if (FastMath.abs(sumExpected - sumObserved) &gt; 10E-6) {<a name="line.102"></a>
<FONT color="green">103</FONT>                ratio = sumObserved / sumExpected;<a name="line.103"></a>
<FONT color="green">104</FONT>                rescale = true;<a name="line.104"></a>
<FONT color="green">105</FONT>            }<a name="line.105"></a>
<FONT color="green">106</FONT>            double sumSq = 0.0d;<a name="line.106"></a>
<FONT color="green">107</FONT>            for (int i = 0; i &lt; observed.length; i++) {<a name="line.107"></a>
<FONT color="green">108</FONT>                if (rescale) {<a name="line.108"></a>
<FONT color="green">109</FONT>                    final double dev = observed[i] - ratio * expected[i];<a name="line.109"></a>
<FONT color="green">110</FONT>                    sumSq += dev * dev / (ratio * expected[i]);<a name="line.110"></a>
<FONT color="green">111</FONT>                } else {<a name="line.111"></a>
<FONT color="green">112</FONT>                    final double dev = observed[i] - expected[i];<a name="line.112"></a>
<FONT color="green">113</FONT>                    sumSq += dev * dev / expected[i];<a name="line.113"></a>
<FONT color="green">114</FONT>                }<a name="line.114"></a>
<FONT color="green">115</FONT>            }<a name="line.115"></a>
<FONT color="green">116</FONT>            return sumSq;<a name="line.116"></a>
<FONT color="green">117</FONT>    <a name="line.117"></a>
<FONT color="green">118</FONT>        }<a name="line.118"></a>
<FONT color="green">119</FONT>    <a name="line.119"></a>
<FONT color="green">120</FONT>        /**<a name="line.120"></a>
<FONT color="green">121</FONT>         * Returns the &lt;i&gt;observed significance level&lt;/i&gt;, or &lt;a href=<a name="line.121"></a>
<FONT color="green">122</FONT>         * "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue"&gt;<a name="line.122"></a>
<FONT color="green">123</FONT>         * p-value&lt;/a&gt;, associated with a<a name="line.123"></a>
<FONT color="green">124</FONT>         * &lt;a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"&gt;<a name="line.124"></a>
<FONT color="green">125</FONT>         * Chi-square goodness of fit test&lt;/a&gt; comparing the &lt;code&gt;observed&lt;/code&gt;<a name="line.125"></a>
<FONT color="green">126</FONT>         * frequency counts to those in the &lt;code&gt;expected&lt;/code&gt; array.<a name="line.126"></a>
<FONT color="green">127</FONT>         * &lt;p&gt;<a name="line.127"></a>
<FONT color="green">128</FONT>         * The number returned is the smallest significance level at which one can reject<a name="line.128"></a>
<FONT color="green">129</FONT>         * the null hypothesis that the observed counts conform to the frequency distribution<a name="line.129"></a>
<FONT color="green">130</FONT>         * described by the expected counts.&lt;/p&gt;<a name="line.130"></a>
<FONT color="green">131</FONT>         * &lt;p&gt;<a name="line.131"></a>
<FONT color="green">132</FONT>         * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.132"></a>
<FONT color="green">133</FONT>         * &lt;li&gt;Expected counts must all be positive.<a name="line.133"></a>
<FONT color="green">134</FONT>         * &lt;/li&gt;<a name="line.134"></a>
<FONT color="green">135</FONT>         * &lt;li&gt;Observed counts must all be &amp;ge; 0.<a name="line.135"></a>
<FONT color="green">136</FONT>         * &lt;/li&gt;<a name="line.136"></a>
<FONT color="green">137</FONT>         * &lt;li&gt;The observed and expected arrays must have the same length and<a name="line.137"></a>
<FONT color="green">138</FONT>         * their common length must be at least 2.<a name="line.138"></a>
<FONT color="green">139</FONT>         * &lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;<a name="line.139"></a>
<FONT color="green">140</FONT>         * If any of the preconditions are not met, an<a name="line.140"></a>
<FONT color="green">141</FONT>         * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.141"></a>
<FONT color="green">142</FONT>         * &lt;p&gt;&lt;strong&gt;Note: &lt;/strong&gt;This implementation rescales the<a name="line.142"></a>
<FONT color="green">143</FONT>         * &lt;code&gt;expected&lt;/code&gt; array if necessary to ensure that the sum of the<a name="line.143"></a>
<FONT color="green">144</FONT>         * expected and observed counts are equal.&lt;/p&gt;<a name="line.144"></a>
<FONT color="green">145</FONT>         *<a name="line.145"></a>
<FONT color="green">146</FONT>         * @param observed array of observed frequency counts<a name="line.146"></a>
<FONT color="green">147</FONT>         * @param expected array of expected frequency counts<a name="line.147"></a>
<FONT color="green">148</FONT>         * @return p-value<a name="line.148"></a>
<FONT color="green">149</FONT>         * @throws NotPositiveException if &lt;code&gt;observed&lt;/code&gt; has negative entries<a name="line.149"></a>
<FONT color="green">150</FONT>         * @throws NotStrictlyPositiveException if &lt;code&gt;expected&lt;/code&gt; has entries that are<a name="line.150"></a>
<FONT color="green">151</FONT>         * not strictly positive<a name="line.151"></a>
<FONT color="green">152</FONT>         * @throws DimensionMismatchException if the arrays length is less than 2<a name="line.152"></a>
<FONT color="green">153</FONT>         * @throws MaxCountExceededException if an error occurs computing the p-value<a name="line.153"></a>
<FONT color="green">154</FONT>         */<a name="line.154"></a>
<FONT color="green">155</FONT>        public double chiSquareTest(final double[] expected, final long[] observed)<a name="line.155"></a>
<FONT color="green">156</FONT>            throws NotPositiveException, NotStrictlyPositiveException,<a name="line.156"></a>
<FONT color="green">157</FONT>            DimensionMismatchException, MaxCountExceededException {<a name="line.157"></a>
<FONT color="green">158</FONT>    <a name="line.158"></a>
<FONT color="green">159</FONT>            ChiSquaredDistribution distribution =<a name="line.159"></a>
<FONT color="green">160</FONT>                new ChiSquaredDistribution(expected.length - 1.0);<a name="line.160"></a>
<FONT color="green">161</FONT>            return 1.0 - distribution.cumulativeProbability(chiSquare(expected, observed));<a name="line.161"></a>
<FONT color="green">162</FONT>        }<a name="line.162"></a>
<FONT color="green">163</FONT>    <a name="line.163"></a>
<FONT color="green">164</FONT>        /**<a name="line.164"></a>
<FONT color="green">165</FONT>         * Performs a &lt;a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda35f.htm"&gt;<a name="line.165"></a>
<FONT color="green">166</FONT>         * Chi-square goodness of fit test&lt;/a&gt; evaluating the null hypothesis that the<a name="line.166"></a>
<FONT color="green">167</FONT>         * observed counts conform to the frequency distribution described by the expected<a name="line.167"></a>
<FONT color="green">168</FONT>         * counts, with significance level &lt;code&gt;alpha&lt;/code&gt;.  Returns true iff the null<a name="line.168"></a>
<FONT color="green">169</FONT>         * hypothesis can be rejected with 100 * (1 - alpha) percent confidence.<a name="line.169"></a>
<FONT color="green">170</FONT>         * &lt;p&gt;<a name="line.170"></a>
<FONT color="green">171</FONT>         * &lt;strong&gt;Example:&lt;/strong&gt;&lt;br&gt;<a name="line.171"></a>
<FONT color="green">172</FONT>         * To test the hypothesis that &lt;code&gt;observed&lt;/code&gt; follows<a name="line.172"></a>
<FONT color="green">173</FONT>         * &lt;code&gt;expected&lt;/code&gt; at the 99% level, use &lt;/p&gt;&lt;p&gt;<a name="line.173"></a>
<FONT color="green">174</FONT>         * &lt;code&gt;chiSquareTest(expected, observed, 0.01) &lt;/code&gt;&lt;/p&gt;<a name="line.174"></a>
<FONT color="green">175</FONT>         * &lt;p&gt;<a name="line.175"></a>
<FONT color="green">176</FONT>         * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.176"></a>
<FONT color="green">177</FONT>         * &lt;li&gt;Expected counts must all be positive.<a name="line.177"></a>
<FONT color="green">178</FONT>         * &lt;/li&gt;<a name="line.178"></a>
<FONT color="green">179</FONT>         * &lt;li&gt;Observed counts must all be &amp;ge; 0.<a name="line.179"></a>
<FONT color="green">180</FONT>         * &lt;/li&gt;<a name="line.180"></a>
<FONT color="green">181</FONT>         * &lt;li&gt;The observed and expected arrays must have the same length and<a name="line.181"></a>
<FONT color="green">182</FONT>         * their common length must be at least 2.<a name="line.182"></a>
<FONT color="green">183</FONT>         * &lt;li&gt; &lt;code&gt; 0 &amp;lt; alpha &amp;lt; 0.5 &lt;/code&gt;<a name="line.183"></a>
<FONT color="green">184</FONT>         * &lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;<a name="line.184"></a>
<FONT color="green">185</FONT>         * If any of the preconditions are not met, an<a name="line.185"></a>
<FONT color="green">186</FONT>         * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.186"></a>
<FONT color="green">187</FONT>         * &lt;p&gt;&lt;strong&gt;Note: &lt;/strong&gt;This implementation rescales the<a name="line.187"></a>
<FONT color="green">188</FONT>         * &lt;code&gt;expected&lt;/code&gt; array if necessary to ensure that the sum of the<a name="line.188"></a>
<FONT color="green">189</FONT>         * expected and observed counts are equal.&lt;/p&gt;<a name="line.189"></a>
<FONT color="green">190</FONT>         *<a name="line.190"></a>
<FONT color="green">191</FONT>         * @param observed array of observed frequency counts<a name="line.191"></a>
<FONT color="green">192</FONT>         * @param expected array of expected frequency counts<a name="line.192"></a>
<FONT color="green">193</FONT>         * @param alpha significance level of the test<a name="line.193"></a>
<FONT color="green">194</FONT>         * @return true iff null hypothesis can be rejected with confidence<a name="line.194"></a>
<FONT color="green">195</FONT>         * 1 - alpha<a name="line.195"></a>
<FONT color="green">196</FONT>         * @throws NotPositiveException if &lt;code&gt;observed&lt;/code&gt; has negative entries<a name="line.196"></a>
<FONT color="green">197</FONT>         * @throws NotStrictlyPositiveException if &lt;code&gt;expected&lt;/code&gt; has entries that are<a name="line.197"></a>
<FONT color="green">198</FONT>         * not strictly positive<a name="line.198"></a>
<FONT color="green">199</FONT>         * @throws DimensionMismatchException if the arrays length is less than 2<a name="line.199"></a>
<FONT color="green">200</FONT>         * @throws OutOfRangeException if &lt;code&gt;alpha&lt;/code&gt; is not in the range (0, 0.5]<a name="line.200"></a>
<FONT color="green">201</FONT>         * @throws MaxCountExceededException if an error occurs computing the p-value<a name="line.201"></a>
<FONT color="green">202</FONT>         */<a name="line.202"></a>
<FONT color="green">203</FONT>        public boolean chiSquareTest(final double[] expected, final long[] observed,<a name="line.203"></a>
<FONT color="green">204</FONT>                                     final double alpha)<a name="line.204"></a>
<FONT color="green">205</FONT>            throws NotPositiveException, NotStrictlyPositiveException,<a name="line.205"></a>
<FONT color="green">206</FONT>            DimensionMismatchException, OutOfRangeException, MaxCountExceededException {<a name="line.206"></a>
<FONT color="green">207</FONT>    <a name="line.207"></a>
<FONT color="green">208</FONT>            if ((alpha &lt;= 0) || (alpha &gt; 0.5)) {<a name="line.208"></a>
<FONT color="green">209</FONT>                throw new OutOfRangeException(LocalizedFormats.OUT_OF_BOUND_SIGNIFICANCE_LEVEL,<a name="line.209"></a>
<FONT color="green">210</FONT>                                              alpha, 0, 0.5);<a name="line.210"></a>
<FONT color="green">211</FONT>            }<a name="line.211"></a>
<FONT color="green">212</FONT>            return chiSquareTest(expected, observed) &lt; alpha;<a name="line.212"></a>
<FONT color="green">213</FONT>    <a name="line.213"></a>
<FONT color="green">214</FONT>        }<a name="line.214"></a>
<FONT color="green">215</FONT>    <a name="line.215"></a>
<FONT color="green">216</FONT>        /**<a name="line.216"></a>
<FONT color="green">217</FONT>         *  Computes the Chi-Square statistic associated with a<a name="line.217"></a>
<FONT color="green">218</FONT>         * &lt;a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"&gt;<a name="line.218"></a>
<FONT color="green">219</FONT>         *  chi-square test of independence&lt;/a&gt; based on the input &lt;code&gt;counts&lt;/code&gt;<a name="line.219"></a>
<FONT color="green">220</FONT>         *  array, viewed as a two-way table.<a name="line.220"></a>
<FONT color="green">221</FONT>         * &lt;p&gt;<a name="line.221"></a>
<FONT color="green">222</FONT>         * The rows of the 2-way table are<a name="line.222"></a>
<FONT color="green">223</FONT>         * &lt;code&gt;count[0], ... , count[count.length - 1] &lt;/code&gt;&lt;/p&gt;<a name="line.223"></a>
<FONT color="green">224</FONT>         * &lt;p&gt;<a name="line.224"></a>
<FONT color="green">225</FONT>         * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.225"></a>
<FONT color="green">226</FONT>         * &lt;li&gt;All counts must be &amp;ge; 0.<a name="line.226"></a>
<FONT color="green">227</FONT>         * &lt;/li&gt;<a name="line.227"></a>
<FONT color="green">228</FONT>         * &lt;li&gt;The count array must be rectangular (i.e. all count[i] subarrays<a name="line.228"></a>
<FONT color="green">229</FONT>         *  must have the same length).<a name="line.229"></a>
<FONT color="green">230</FONT>         * &lt;/li&gt;<a name="line.230"></a>
<FONT color="green">231</FONT>         * &lt;li&gt;The 2-way table represented by &lt;code&gt;counts&lt;/code&gt; must have at<a name="line.231"></a>
<FONT color="green">232</FONT>         *  least 2 columns and at least 2 rows.<a name="line.232"></a>
<FONT color="green">233</FONT>         * &lt;/li&gt;<a name="line.233"></a>
<FONT color="green">234</FONT>         * &lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;<a name="line.234"></a>
<FONT color="green">235</FONT>         * If any of the preconditions are not met, an<a name="line.235"></a>
<FONT color="green">236</FONT>         * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.236"></a>
<FONT color="green">237</FONT>         *<a name="line.237"></a>
<FONT color="green">238</FONT>         * @param counts array representation of 2-way table<a name="line.238"></a>
<FONT color="green">239</FONT>         * @return chiSquare test statistic<a name="line.239"></a>
<FONT color="green">240</FONT>         * @throws NullArgumentException if the array is null<a name="line.240"></a>
<FONT color="green">241</FONT>         * @throws DimensionMismatchException if the array is not rectangular<a name="line.241"></a>
<FONT color="green">242</FONT>         * @throws NotPositiveException if {@code counts} has negative entries<a name="line.242"></a>
<FONT color="green">243</FONT>         */<a name="line.243"></a>
<FONT color="green">244</FONT>        public double chiSquare(final long[][] counts)<a name="line.244"></a>
<FONT color="green">245</FONT>            throws NullArgumentException, NotPositiveException,<a name="line.245"></a>
<FONT color="green">246</FONT>            DimensionMismatchException {<a name="line.246"></a>
<FONT color="green">247</FONT>    <a name="line.247"></a>
<FONT color="green">248</FONT>            checkArray(counts);<a name="line.248"></a>
<FONT color="green">249</FONT>            int nRows = counts.length;<a name="line.249"></a>
<FONT color="green">250</FONT>            int nCols = counts[0].length;<a name="line.250"></a>
<FONT color="green">251</FONT>    <a name="line.251"></a>
<FONT color="green">252</FONT>            // compute row, column and total sums<a name="line.252"></a>
<FONT color="green">253</FONT>            double[] rowSum = new double[nRows];<a name="line.253"></a>
<FONT color="green">254</FONT>            double[] colSum = new double[nCols];<a name="line.254"></a>
<FONT color="green">255</FONT>            double total = 0.0d;<a name="line.255"></a>
<FONT color="green">256</FONT>            for (int row = 0; row &lt; nRows; row++) {<a name="line.256"></a>
<FONT color="green">257</FONT>                for (int col = 0; col &lt; nCols; col++) {<a name="line.257"></a>
<FONT color="green">258</FONT>                    rowSum[row] += counts[row][col];<a name="line.258"></a>
<FONT color="green">259</FONT>                    colSum[col] += counts[row][col];<a name="line.259"></a>
<FONT color="green">260</FONT>                    total += counts[row][col];<a name="line.260"></a>
<FONT color="green">261</FONT>                }<a name="line.261"></a>
<FONT color="green">262</FONT>            }<a name="line.262"></a>
<FONT color="green">263</FONT>    <a name="line.263"></a>
<FONT color="green">264</FONT>            // compute expected counts and chi-square<a name="line.264"></a>
<FONT color="green">265</FONT>            double sumSq = 0.0d;<a name="line.265"></a>
<FONT color="green">266</FONT>            double expected = 0.0d;<a name="line.266"></a>
<FONT color="green">267</FONT>            for (int row = 0; row &lt; nRows; row++) {<a name="line.267"></a>
<FONT color="green">268</FONT>                for (int col = 0; col &lt; nCols; col++) {<a name="line.268"></a>
<FONT color="green">269</FONT>                    expected = (rowSum[row] * colSum[col]) / total;<a name="line.269"></a>
<FONT color="green">270</FONT>                    sumSq += ((counts[row][col] - expected) *<a name="line.270"></a>
<FONT color="green">271</FONT>                            (counts[row][col] - expected)) / expected;<a name="line.271"></a>
<FONT color="green">272</FONT>                }<a name="line.272"></a>
<FONT color="green">273</FONT>            }<a name="line.273"></a>
<FONT color="green">274</FONT>            return sumSq;<a name="line.274"></a>
<FONT color="green">275</FONT>    <a name="line.275"></a>
<FONT color="green">276</FONT>        }<a name="line.276"></a>
<FONT color="green">277</FONT>    <a name="line.277"></a>
<FONT color="green">278</FONT>        /**<a name="line.278"></a>
<FONT color="green">279</FONT>         * Returns the &lt;i&gt;observed significance level&lt;/i&gt;, or &lt;a href=<a name="line.279"></a>
<FONT color="green">280</FONT>         * "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue"&gt;<a name="line.280"></a>
<FONT color="green">281</FONT>         * p-value&lt;/a&gt;, associated with a<a name="line.281"></a>
<FONT color="green">282</FONT>         * &lt;a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"&gt;<a name="line.282"></a>
<FONT color="green">283</FONT>         * chi-square test of independence&lt;/a&gt; based on the input &lt;code&gt;counts&lt;/code&gt;<a name="line.283"></a>
<FONT color="green">284</FONT>         * array, viewed as a two-way table.<a name="line.284"></a>
<FONT color="green">285</FONT>         * &lt;p&gt;<a name="line.285"></a>
<FONT color="green">286</FONT>         * The rows of the 2-way table are<a name="line.286"></a>
<FONT color="green">287</FONT>         * &lt;code&gt;count[0], ... , count[count.length - 1] &lt;/code&gt;&lt;/p&gt;<a name="line.287"></a>
<FONT color="green">288</FONT>         * &lt;p&gt;<a name="line.288"></a>
<FONT color="green">289</FONT>         * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.289"></a>
<FONT color="green">290</FONT>         * &lt;li&gt;All counts must be &amp;ge; 0.<a name="line.290"></a>
<FONT color="green">291</FONT>         * &lt;/li&gt;<a name="line.291"></a>
<FONT color="green">292</FONT>         * &lt;li&gt;The count array must be rectangular (i.e. all count[i] subarrays must have<a name="line.292"></a>
<FONT color="green">293</FONT>         *     the same length).<a name="line.293"></a>
<FONT color="green">294</FONT>         * &lt;/li&gt;<a name="line.294"></a>
<FONT color="green">295</FONT>         * &lt;li&gt;The 2-way table represented by &lt;code&gt;counts&lt;/code&gt; must have at least 2<a name="line.295"></a>
<FONT color="green">296</FONT>         *     columns and at least 2 rows.<a name="line.296"></a>
<FONT color="green">297</FONT>         * &lt;/li&gt;<a name="line.297"></a>
<FONT color="green">298</FONT>         * &lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;<a name="line.298"></a>
<FONT color="green">299</FONT>         * If any of the preconditions are not met, an<a name="line.299"></a>
<FONT color="green">300</FONT>         * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.300"></a>
<FONT color="green">301</FONT>         *<a name="line.301"></a>
<FONT color="green">302</FONT>         * @param counts array representation of 2-way table<a name="line.302"></a>
<FONT color="green">303</FONT>         * @return p-value<a name="line.303"></a>
<FONT color="green">304</FONT>         * @throws NullArgumentException if the array is null<a name="line.304"></a>
<FONT color="green">305</FONT>         * @throws DimensionMismatchException if the array is not rectangular<a name="line.305"></a>
<FONT color="green">306</FONT>         * @throws NotPositiveException if {@code counts} has negative entries<a name="line.306"></a>
<FONT color="green">307</FONT>         * @throws MaxCountExceededException if an error occurs computing the p-value<a name="line.307"></a>
<FONT color="green">308</FONT>         */<a name="line.308"></a>
<FONT color="green">309</FONT>        public double chiSquareTest(final long[][] counts)<a name="line.309"></a>
<FONT color="green">310</FONT>            throws NullArgumentException, DimensionMismatchException,<a name="line.310"></a>
<FONT color="green">311</FONT>            NotPositiveException, MaxCountExceededException {<a name="line.311"></a>
<FONT color="green">312</FONT>    <a name="line.312"></a>
<FONT color="green">313</FONT>            checkArray(counts);<a name="line.313"></a>
<FONT color="green">314</FONT>            double df = ((double) counts.length -1) * ((double) counts[0].length - 1);<a name="line.314"></a>
<FONT color="green">315</FONT>            ChiSquaredDistribution distribution;<a name="line.315"></a>
<FONT color="green">316</FONT>            distribution = new ChiSquaredDistribution(df);<a name="line.316"></a>
<FONT color="green">317</FONT>            return 1 - distribution.cumulativeProbability(chiSquare(counts));<a name="line.317"></a>
<FONT color="green">318</FONT>    <a name="line.318"></a>
<FONT color="green">319</FONT>        }<a name="line.319"></a>
<FONT color="green">320</FONT>    <a name="line.320"></a>
<FONT color="green">321</FONT>        /**<a name="line.321"></a>
<FONT color="green">322</FONT>         * Performs a &lt;a href="http://www.itl.nist.gov/div898/handbook/prc/section4/prc45.htm"&gt;<a name="line.322"></a>
<FONT color="green">323</FONT>         * chi-square test of independence&lt;/a&gt; evaluating the null hypothesis that the<a name="line.323"></a>
<FONT color="green">324</FONT>         * classifications represented by the counts in the columns of the input 2-way table<a name="line.324"></a>
<FONT color="green">325</FONT>         * are independent of the rows, with significance level &lt;code&gt;alpha&lt;/code&gt;.<a name="line.325"></a>
<FONT color="green">326</FONT>         * Returns true iff the null hypothesis can be rejected with 100 * (1 - alpha) percent<a name="line.326"></a>
<FONT color="green">327</FONT>         * confidence.<a name="line.327"></a>
<FONT color="green">328</FONT>         * &lt;p&gt;<a name="line.328"></a>
<FONT color="green">329</FONT>         * The rows of the 2-way table are<a name="line.329"></a>
<FONT color="green">330</FONT>         * &lt;code&gt;count[0], ... , count[count.length - 1] &lt;/code&gt;&lt;/p&gt;<a name="line.330"></a>
<FONT color="green">331</FONT>         * &lt;p&gt;<a name="line.331"></a>
<FONT color="green">332</FONT>         * &lt;strong&gt;Example:&lt;/strong&gt;&lt;br&gt;<a name="line.332"></a>
<FONT color="green">333</FONT>         * To test the null hypothesis that the counts in<a name="line.333"></a>
<FONT color="green">334</FONT>         * &lt;code&gt;count[0], ... , count[count.length - 1] &lt;/code&gt;<a name="line.334"></a>
<FONT color="green">335</FONT>         *  all correspond to the same underlying probability distribution at the 99% level, use&lt;/p&gt;<a name="line.335"></a>
<FONT color="green">336</FONT>         * &lt;p&gt;&lt;code&gt;chiSquareTest(counts, 0.01)&lt;/code&gt;&lt;/p&gt;<a name="line.336"></a>
<FONT color="green">337</FONT>         * &lt;p&gt;<a name="line.337"></a>
<FONT color="green">338</FONT>         * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.338"></a>
<FONT color="green">339</FONT>         * &lt;li&gt;All counts must be &amp;ge; 0.<a name="line.339"></a>
<FONT color="green">340</FONT>         * &lt;/li&gt;<a name="line.340"></a>
<FONT color="green">341</FONT>         * &lt;li&gt;The count array must be rectangular (i.e. all count[i] subarrays must have the<a name="line.341"></a>
<FONT color="green">342</FONT>         *     same length).&lt;/li&gt;<a name="line.342"></a>
<FONT color="green">343</FONT>         * &lt;li&gt;The 2-way table represented by &lt;code&gt;counts&lt;/code&gt; must have at least 2 columns and<a name="line.343"></a>
<FONT color="green">344</FONT>         *     at least 2 rows.&lt;/li&gt;<a name="line.344"></a>
<FONT color="green">345</FONT>         * &lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;<a name="line.345"></a>
<FONT color="green">346</FONT>         * If any of the preconditions are not met, an<a name="line.346"></a>
<FONT color="green">347</FONT>         * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.347"></a>
<FONT color="green">348</FONT>         *<a name="line.348"></a>
<FONT color="green">349</FONT>         * @param counts array representation of 2-way table<a name="line.349"></a>
<FONT color="green">350</FONT>         * @param alpha significance level of the test<a name="line.350"></a>
<FONT color="green">351</FONT>         * @return true iff null hypothesis can be rejected with confidence<a name="line.351"></a>
<FONT color="green">352</FONT>         * 1 - alpha<a name="line.352"></a>
<FONT color="green">353</FONT>         * @throws NullArgumentException if the array is null<a name="line.353"></a>
<FONT color="green">354</FONT>         * @throws DimensionMismatchException if the array is not rectangular<a name="line.354"></a>
<FONT color="green">355</FONT>         * @throws NotPositiveException if {@code counts} has any negative entries<a name="line.355"></a>
<FONT color="green">356</FONT>         * @throws OutOfRangeException if &lt;code&gt;alpha&lt;/code&gt; is not in the range (0, 0.5]<a name="line.356"></a>
<FONT color="green">357</FONT>         * @throws MaxCountExceededException if an error occurs computing the p-value<a name="line.357"></a>
<FONT color="green">358</FONT>         */<a name="line.358"></a>
<FONT color="green">359</FONT>        public boolean chiSquareTest(final long[][] counts, final double alpha)<a name="line.359"></a>
<FONT color="green">360</FONT>            throws NullArgumentException, DimensionMismatchException,<a name="line.360"></a>
<FONT color="green">361</FONT>            NotPositiveException, OutOfRangeException, MaxCountExceededException {<a name="line.361"></a>
<FONT color="green">362</FONT>    <a name="line.362"></a>
<FONT color="green">363</FONT>            if ((alpha &lt;= 0) || (alpha &gt; 0.5)) {<a name="line.363"></a>
<FONT color="green">364</FONT>                throw new OutOfRangeException(LocalizedFormats.OUT_OF_BOUND_SIGNIFICANCE_LEVEL,<a name="line.364"></a>
<FONT color="green">365</FONT>                                              alpha, 0, 0.5);<a name="line.365"></a>
<FONT color="green">366</FONT>            }<a name="line.366"></a>
<FONT color="green">367</FONT>            return chiSquareTest(counts) &lt; alpha;<a name="line.367"></a>
<FONT color="green">368</FONT>    <a name="line.368"></a>
<FONT color="green">369</FONT>        }<a name="line.369"></a>
<FONT color="green">370</FONT>    <a name="line.370"></a>
<FONT color="green">371</FONT>        /**<a name="line.371"></a>
<FONT color="green">372</FONT>         * &lt;p&gt;Computes a<a name="line.372"></a>
<FONT color="green">373</FONT>         * &lt;a href="http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/chi2samp.htm"&gt;<a name="line.373"></a>
<FONT color="green">374</FONT>         * Chi-Square two sample test statistic&lt;/a&gt; comparing bin frequency counts<a name="line.374"></a>
<FONT color="green">375</FONT>         * in &lt;code&gt;observed1&lt;/code&gt; and &lt;code&gt;observed2&lt;/code&gt;.  The<a name="line.375"></a>
<FONT color="green">376</FONT>         * sums of frequency counts in the two samples are not required to be the<a name="line.376"></a>
<FONT color="green">377</FONT>         * same.  The formula used to compute the test statistic is&lt;/p&gt;<a name="line.377"></a>
<FONT color="green">378</FONT>         * &lt;code&gt;<a name="line.378"></a>
<FONT color="green">379</FONT>         * &amp;sum;[(K * observed1[i] - observed2[i]/K)&lt;sup&gt;2&lt;/sup&gt; / (observed1[i] + observed2[i])]<a name="line.379"></a>
<FONT color="green">380</FONT>         * &lt;/code&gt; where<a name="line.380"></a>
<FONT color="green">381</FONT>         * &lt;br/&gt;&lt;code&gt;K = &amp;sqrt;[&amp;sum(observed2 / &amp;sum;(observed1)]&lt;/code&gt;<a name="line.381"></a>
<FONT color="green">382</FONT>         * &lt;/p&gt;<a name="line.382"></a>
<FONT color="green">383</FONT>         * &lt;p&gt;This statistic can be used to perform a Chi-Square test evaluating the<a name="line.383"></a>
<FONT color="green">384</FONT>         * null hypothesis that both observed counts follow the same distribution.&lt;/p&gt;<a name="line.384"></a>
<FONT color="green">385</FONT>         * &lt;p&gt;<a name="line.385"></a>
<FONT color="green">386</FONT>         * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.386"></a>
<FONT color="green">387</FONT>         * &lt;li&gt;Observed counts must be non-negative.<a name="line.387"></a>
<FONT color="green">388</FONT>         * &lt;/li&gt;<a name="line.388"></a>
<FONT color="green">389</FONT>         * &lt;li&gt;Observed counts for a specific bin must not both be zero.<a name="line.389"></a>
<FONT color="green">390</FONT>         * &lt;/li&gt;<a name="line.390"></a>
<FONT color="green">391</FONT>         * &lt;li&gt;Observed counts for a specific sample must not all be 0.<a name="line.391"></a>
<FONT color="green">392</FONT>         * &lt;/li&gt;<a name="line.392"></a>
<FONT color="green">393</FONT>         * &lt;li&gt;The arrays &lt;code&gt;observed1&lt;/code&gt; and &lt;code&gt;observed2&lt;/code&gt; must have<a name="line.393"></a>
<FONT color="green">394</FONT>         * the same length and their common length must be at least 2.<a name="line.394"></a>
<FONT color="green">395</FONT>         * &lt;/li&gt;&lt;/ul&gt;&lt;/p&gt;&lt;p&gt;<a name="line.395"></a>
<FONT color="green">396</FONT>         * If any of the preconditions are not met, an<a name="line.396"></a>
<FONT color="green">397</FONT>         * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.397"></a>
<FONT color="green">398</FONT>         *<a name="line.398"></a>
<FONT color="green">399</FONT>         * @param observed1 array of observed frequency counts of the first data set<a name="line.399"></a>
<FONT color="green">400</FONT>         * @param observed2 array of observed frequency counts of the second data set<a name="line.400"></a>
<FONT color="green">401</FONT>         * @return chiSquare test statistic<a name="line.401"></a>
<FONT color="green">402</FONT>         * @throws DimensionMismatchException the the length of the arrays does not match<a name="line.402"></a>
<FONT color="green">403</FONT>         * @throws NotPositiveException if any entries in &lt;code&gt;observed1&lt;/code&gt; or<a name="line.403"></a>
<FONT color="green">404</FONT>         * &lt;code&gt;observed2&lt;/code&gt; are negative<a name="line.404"></a>
<FONT color="green">405</FONT>         * @throws ZeroException if either all counts of &lt;code&gt;observed1&lt;/code&gt; or<a name="line.405"></a>
<FONT color="green">406</FONT>         * &lt;code&gt;observed2&lt;/code&gt; are zero, or if the count at some index is zero<a name="line.406"></a>
<FONT color="green">407</FONT>         * for both arrays<a name="line.407"></a>
<FONT color="green">408</FONT>         * @since 1.2<a name="line.408"></a>
<FONT color="green">409</FONT>         */<a name="line.409"></a>
<FONT color="green">410</FONT>        public double chiSquareDataSetsComparison(long[] observed1, long[] observed2)<a name="line.410"></a>
<FONT color="green">411</FONT>            throws DimensionMismatchException, NotPositiveException, ZeroException {<a name="line.411"></a>
<FONT color="green">412</FONT>    <a name="line.412"></a>
<FONT color="green">413</FONT>            // Make sure lengths are same<a name="line.413"></a>
<FONT color="green">414</FONT>            if (observed1.length &lt; 2) {<a name="line.414"></a>
<FONT color="green">415</FONT>                throw new DimensionMismatchException(observed1.length, 2);<a name="line.415"></a>
<FONT color="green">416</FONT>            }<a name="line.416"></a>
<FONT color="green">417</FONT>            if (observed1.length != observed2.length) {<a name="line.417"></a>
<FONT color="green">418</FONT>                throw new DimensionMismatchException(observed1.length, observed2.length);<a name="line.418"></a>
<FONT color="green">419</FONT>            }<a name="line.419"></a>
<FONT color="green">420</FONT>    <a name="line.420"></a>
<FONT color="green">421</FONT>            // Ensure non-negative counts<a name="line.421"></a>
<FONT color="green">422</FONT>            MathArrays.checkNonNegative(observed1);<a name="line.422"></a>
<FONT color="green">423</FONT>            MathArrays.checkNonNegative(observed2);<a name="line.423"></a>
<FONT color="green">424</FONT>    <a name="line.424"></a>
<FONT color="green">425</FONT>            // Compute and compare count sums<a name="line.425"></a>
<FONT color="green">426</FONT>            long countSum1 = 0;<a name="line.426"></a>
<FONT color="green">427</FONT>            long countSum2 = 0;<a name="line.427"></a>
<FONT color="green">428</FONT>            boolean unequalCounts = false;<a name="line.428"></a>
<FONT color="green">429</FONT>            double weight = 0.0;<a name="line.429"></a>
<FONT color="green">430</FONT>            for (int i = 0; i &lt; observed1.length; i++) {<a name="line.430"></a>
<FONT color="green">431</FONT>                countSum1 += observed1[i];<a name="line.431"></a>
<FONT color="green">432</FONT>                countSum2 += observed2[i];<a name="line.432"></a>
<FONT color="green">433</FONT>            }<a name="line.433"></a>
<FONT color="green">434</FONT>            // Ensure neither sample is uniformly 0<a name="line.434"></a>
<FONT color="green">435</FONT>            if (countSum1 == 0 || countSum2 == 0) {<a name="line.435"></a>
<FONT color="green">436</FONT>                throw new ZeroException();<a name="line.436"></a>
<FONT color="green">437</FONT>            }<a name="line.437"></a>
<FONT color="green">438</FONT>            // Compare and compute weight only if different<a name="line.438"></a>
<FONT color="green">439</FONT>            unequalCounts = countSum1 != countSum2;<a name="line.439"></a>
<FONT color="green">440</FONT>            if (unequalCounts) {<a name="line.440"></a>
<FONT color="green">441</FONT>                weight = FastMath.sqrt((double) countSum1 / (double) countSum2);<a name="line.441"></a>
<FONT color="green">442</FONT>            }<a name="line.442"></a>
<FONT color="green">443</FONT>            // Compute ChiSquare statistic<a name="line.443"></a>
<FONT color="green">444</FONT>            double sumSq = 0.0d;<a name="line.444"></a>
<FONT color="green">445</FONT>            double dev = 0.0d;<a name="line.445"></a>
<FONT color="green">446</FONT>            double obs1 = 0.0d;<a name="line.446"></a>
<FONT color="green">447</FONT>            double obs2 = 0.0d;<a name="line.447"></a>
<FONT color="green">448</FONT>            for (int i = 0; i &lt; observed1.length; i++) {<a name="line.448"></a>
<FONT color="green">449</FONT>                if (observed1[i] == 0 &amp;&amp; observed2[i] == 0) {<a name="line.449"></a>
<FONT color="green">450</FONT>                    throw new ZeroException(LocalizedFormats.OBSERVED_COUNTS_BOTTH_ZERO_FOR_ENTRY, i);<a name="line.450"></a>
<FONT color="green">451</FONT>                } else {<a name="line.451"></a>
<FONT color="green">452</FONT>                    obs1 = observed1[i];<a name="line.452"></a>
<FONT color="green">453</FONT>                    obs2 = observed2[i];<a name="line.453"></a>
<FONT color="green">454</FONT>                    if (unequalCounts) { // apply weights<a name="line.454"></a>
<FONT color="green">455</FONT>                        dev = obs1/weight - obs2 * weight;<a name="line.455"></a>
<FONT color="green">456</FONT>                    } else {<a name="line.456"></a>
<FONT color="green">457</FONT>                        dev = obs1 - obs2;<a name="line.457"></a>
<FONT color="green">458</FONT>                    }<a name="line.458"></a>
<FONT color="green">459</FONT>                    sumSq += (dev * dev) / (obs1 + obs2);<a name="line.459"></a>
<FONT color="green">460</FONT>                }<a name="line.460"></a>
<FONT color="green">461</FONT>            }<a name="line.461"></a>
<FONT color="green">462</FONT>            return sumSq;<a name="line.462"></a>
<FONT color="green">463</FONT>        }<a name="line.463"></a>
<FONT color="green">464</FONT>    <a name="line.464"></a>
<FONT color="green">465</FONT>        /**<a name="line.465"></a>
<FONT color="green">466</FONT>         * &lt;p&gt;Returns the &lt;i&gt;observed significance level&lt;/i&gt;, or &lt;a href=<a name="line.466"></a>
<FONT color="green">467</FONT>         * "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue"&gt;<a name="line.467"></a>
<FONT color="green">468</FONT>         * p-value&lt;/a&gt;, associated with a Chi-Square two sample test comparing<a name="line.468"></a>
<FONT color="green">469</FONT>         * bin frequency counts in &lt;code&gt;observed1&lt;/code&gt; and<a name="line.469"></a>
<FONT color="green">470</FONT>         * &lt;code&gt;observed2&lt;/code&gt;.<a name="line.470"></a>
<FONT color="green">471</FONT>         * &lt;/p&gt;<a name="line.471"></a>
<FONT color="green">472</FONT>         * &lt;p&gt;The number returned is the smallest significance level at which one<a name="line.472"></a>
<FONT color="green">473</FONT>         * can reject the null hypothesis that the observed counts conform to the<a name="line.473"></a>
<FONT color="green">474</FONT>         * same distribution.<a name="line.474"></a>
<FONT color="green">475</FONT>         * &lt;/p&gt;<a name="line.475"></a>
<FONT color="green">476</FONT>         * &lt;p&gt;See {@link #chiSquareDataSetsComparison(long[], long[])} for details<a name="line.476"></a>
<FONT color="green">477</FONT>         * on the formula used to compute the test statistic. The degrees of<a name="line.477"></a>
<FONT color="green">478</FONT>         * of freedom used to perform the test is one less than the common length<a name="line.478"></a>
<FONT color="green">479</FONT>         * of the input observed count arrays.<a name="line.479"></a>
<FONT color="green">480</FONT>         * &lt;/p&gt;<a name="line.480"></a>
<FONT color="green">481</FONT>         * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.481"></a>
<FONT color="green">482</FONT>         * &lt;li&gt;Observed counts must be non-negative.<a name="line.482"></a>
<FONT color="green">483</FONT>         * &lt;/li&gt;<a name="line.483"></a>
<FONT color="green">484</FONT>         * &lt;li&gt;Observed counts for a specific bin must not both be zero.<a name="line.484"></a>
<FONT color="green">485</FONT>         * &lt;/li&gt;<a name="line.485"></a>
<FONT color="green">486</FONT>         * &lt;li&gt;Observed counts for a specific sample must not all be 0.<a name="line.486"></a>
<FONT color="green">487</FONT>         * &lt;/li&gt;<a name="line.487"></a>
<FONT color="green">488</FONT>         * &lt;li&gt;The arrays &lt;code&gt;observed1&lt;/code&gt; and &lt;code&gt;observed2&lt;/code&gt; must<a name="line.488"></a>
<FONT color="green">489</FONT>         * have the same length and<a name="line.489"></a>
<FONT color="green">490</FONT>         * their common length must be at least 2.<a name="line.490"></a>
<FONT color="green">491</FONT>         * &lt;/li&gt;&lt;/ul&gt;&lt;p&gt;<a name="line.491"></a>
<FONT color="green">492</FONT>         * If any of the preconditions are not met, an<a name="line.492"></a>
<FONT color="green">493</FONT>         * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.493"></a>
<FONT color="green">494</FONT>         *<a name="line.494"></a>
<FONT color="green">495</FONT>         * @param observed1 array of observed frequency counts of the first data set<a name="line.495"></a>
<FONT color="green">496</FONT>         * @param observed2 array of observed frequency counts of the second data set<a name="line.496"></a>
<FONT color="green">497</FONT>         * @return p-value<a name="line.497"></a>
<FONT color="green">498</FONT>         * @throws DimensionMismatchException the the length of the arrays does not match<a name="line.498"></a>
<FONT color="green">499</FONT>         * @throws NotPositiveException if any entries in &lt;code&gt;observed1&lt;/code&gt; or<a name="line.499"></a>
<FONT color="green">500</FONT>         * &lt;code&gt;observed2&lt;/code&gt; are negative<a name="line.500"></a>
<FONT color="green">501</FONT>         * @throws ZeroException if either all counts of &lt;code&gt;observed1&lt;/code&gt; or<a name="line.501"></a>
<FONT color="green">502</FONT>         * &lt;code&gt;observed2&lt;/code&gt; are zero, or if the count at the same index is zero<a name="line.502"></a>
<FONT color="green">503</FONT>         * for both arrays<a name="line.503"></a>
<FONT color="green">504</FONT>         * @throws MaxCountExceededException if an error occurs computing the p-value<a name="line.504"></a>
<FONT color="green">505</FONT>         * @since 1.2<a name="line.505"></a>
<FONT color="green">506</FONT>         */<a name="line.506"></a>
<FONT color="green">507</FONT>        public double chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)<a name="line.507"></a>
<FONT color="green">508</FONT>            throws DimensionMismatchException, NotPositiveException, ZeroException,<a name="line.508"></a>
<FONT color="green">509</FONT>            MaxCountExceededException {<a name="line.509"></a>
<FONT color="green">510</FONT>    <a name="line.510"></a>
<FONT color="green">511</FONT>            ChiSquaredDistribution distribution;<a name="line.511"></a>
<FONT color="green">512</FONT>            distribution = new ChiSquaredDistribution((double) observed1.length - 1);<a name="line.512"></a>
<FONT color="green">513</FONT>            return 1 - distribution.cumulativeProbability(<a name="line.513"></a>
<FONT color="green">514</FONT>                    chiSquareDataSetsComparison(observed1, observed2));<a name="line.514"></a>
<FONT color="green">515</FONT>    <a name="line.515"></a>
<FONT color="green">516</FONT>        }<a name="line.516"></a>
<FONT color="green">517</FONT>    <a name="line.517"></a>
<FONT color="green">518</FONT>        /**<a name="line.518"></a>
<FONT color="green">519</FONT>         * &lt;p&gt;Performs a Chi-Square two sample test comparing two binned data<a name="line.519"></a>
<FONT color="green">520</FONT>         * sets. The test evaluates the null hypothesis that the two lists of<a name="line.520"></a>
<FONT color="green">521</FONT>         * observed counts conform to the same frequency distribution, with<a name="line.521"></a>
<FONT color="green">522</FONT>         * significance level &lt;code&gt;alpha&lt;/code&gt;.  Returns true iff the null<a name="line.522"></a>
<FONT color="green">523</FONT>         * hypothesis can be rejected with 100 * (1 - alpha) percent confidence.<a name="line.523"></a>
<FONT color="green">524</FONT>         * &lt;/p&gt;<a name="line.524"></a>
<FONT color="green">525</FONT>         * &lt;p&gt;See {@link #chiSquareDataSetsComparison(long[], long[])} for<a name="line.525"></a>
<FONT color="green">526</FONT>         * details on the formula used to compute the Chisquare statistic used<a name="line.526"></a>
<FONT color="green">527</FONT>         * in the test. The degrees of of freedom used to perform the test is<a name="line.527"></a>
<FONT color="green">528</FONT>         * one less than the common length of the input observed count arrays.<a name="line.528"></a>
<FONT color="green">529</FONT>         * &lt;/p&gt;<a name="line.529"></a>
<FONT color="green">530</FONT>         * &lt;strong&gt;Preconditions&lt;/strong&gt;: &lt;ul&gt;<a name="line.530"></a>
<FONT color="green">531</FONT>         * &lt;li&gt;Observed counts must be non-negative.<a name="line.531"></a>
<FONT color="green">532</FONT>         * &lt;/li&gt;<a name="line.532"></a>
<FONT color="green">533</FONT>         * &lt;li&gt;Observed counts for a specific bin must not both be zero.<a name="line.533"></a>
<FONT color="green">534</FONT>         * &lt;/li&gt;<a name="line.534"></a>
<FONT color="green">535</FONT>         * &lt;li&gt;Observed counts for a specific sample must not all be 0.<a name="line.535"></a>
<FONT color="green">536</FONT>         * &lt;/li&gt;<a name="line.536"></a>
<FONT color="green">537</FONT>         * &lt;li&gt;The arrays &lt;code&gt;observed1&lt;/code&gt; and &lt;code&gt;observed2&lt;/code&gt; must<a name="line.537"></a>
<FONT color="green">538</FONT>         * have the same length and their common length must be at least 2.<a name="line.538"></a>
<FONT color="green">539</FONT>         * &lt;/li&gt;<a name="line.539"></a>
<FONT color="green">540</FONT>         * &lt;li&gt; &lt;code&gt; 0 &lt; alpha &lt; 0.5 &lt;/code&gt;<a name="line.540"></a>
<FONT color="green">541</FONT>         * &lt;/li&gt;&lt;/ul&gt;&lt;p&gt;<a name="line.541"></a>
<FONT color="green">542</FONT>         * If any of the preconditions are not met, an<a name="line.542"></a>
<FONT color="green">543</FONT>         * &lt;code&gt;IllegalArgumentException&lt;/code&gt; is thrown.&lt;/p&gt;<a name="line.543"></a>
<FONT color="green">544</FONT>         *<a name="line.544"></a>
<FONT color="green">545</FONT>         * @param observed1 array of observed frequency counts of the first data set<a name="line.545"></a>
<FONT color="green">546</FONT>         * @param observed2 array of observed frequency counts of the second data set<a name="line.546"></a>
<FONT color="green">547</FONT>         * @param alpha significance level of the test<a name="line.547"></a>
<FONT color="green">548</FONT>         * @return true iff null hypothesis can be rejected with confidence<a name="line.548"></a>
<FONT color="green">549</FONT>         * 1 - alpha<a name="line.549"></a>
<FONT color="green">550</FONT>         * @throws DimensionMismatchException the the length of the arrays does not match<a name="line.550"></a>
<FONT color="green">551</FONT>         * @throws NotPositiveException if any entries in &lt;code&gt;observed1&lt;/code&gt; or<a name="line.551"></a>
<FONT color="green">552</FONT>         * &lt;code&gt;observed2&lt;/code&gt; are negative<a name="line.552"></a>
<FONT color="green">553</FONT>         * @throws ZeroException if either all counts of &lt;code&gt;observed1&lt;/code&gt; or<a name="line.553"></a>
<FONT color="green">554</FONT>         * &lt;code&gt;observed2&lt;/code&gt; are zero, or if the count at the same index is zero<a name="line.554"></a>
<FONT color="green">555</FONT>         * for both arrays<a name="line.555"></a>
<FONT color="green">556</FONT>         * @throws OutOfRangeException if &lt;code&gt;alpha&lt;/code&gt; is not in the range (0, 0.5]<a name="line.556"></a>
<FONT color="green">557</FONT>         * @throws MaxCountExceededException if an error occurs performing the test<a name="line.557"></a>
<FONT color="green">558</FONT>         * @since 1.2<a name="line.558"></a>
<FONT color="green">559</FONT>         */<a name="line.559"></a>
<FONT color="green">560</FONT>        public boolean chiSquareTestDataSetsComparison(final long[] observed1,<a name="line.560"></a>
<FONT color="green">561</FONT>                                                       final long[] observed2,<a name="line.561"></a>
<FONT color="green">562</FONT>                                                       final double alpha)<a name="line.562"></a>
<FONT color="green">563</FONT>            throws DimensionMismatchException, NotPositiveException,<a name="line.563"></a>
<FONT color="green">564</FONT>            ZeroException, OutOfRangeException, MaxCountExceededException {<a name="line.564"></a>
<FONT color="green">565</FONT>    <a name="line.565"></a>
<FONT color="green">566</FONT>            if (alpha &lt;= 0 ||<a name="line.566"></a>
<FONT color="green">567</FONT>                alpha &gt; 0.5) {<a name="line.567"></a>
<FONT color="green">568</FONT>                throw new OutOfRangeException(LocalizedFormats.OUT_OF_BOUND_SIGNIFICANCE_LEVEL,<a name="line.568"></a>
<FONT color="green">569</FONT>                                              alpha, 0, 0.5);<a name="line.569"></a>
<FONT color="green">570</FONT>            }<a name="line.570"></a>
<FONT color="green">571</FONT>            return chiSquareTestDataSetsComparison(observed1, observed2) &lt; alpha;<a name="line.571"></a>
<FONT color="green">572</FONT>    <a name="line.572"></a>
<FONT color="green">573</FONT>        }<a name="line.573"></a>
<FONT color="green">574</FONT>    <a name="line.574"></a>
<FONT color="green">575</FONT>        /**<a name="line.575"></a>
<FONT color="green">576</FONT>         * Checks to make sure that the input long[][] array is rectangular,<a name="line.576"></a>
<FONT color="green">577</FONT>         * has at least 2 rows and 2 columns, and has all non-negative entries.<a name="line.577"></a>
<FONT color="green">578</FONT>         *<a name="line.578"></a>
<FONT color="green">579</FONT>         * @param in input 2-way table to check<a name="line.579"></a>
<FONT color="green">580</FONT>         * @throws NullArgumentException if the array is null<a name="line.580"></a>
<FONT color="green">581</FONT>         * @throws DimensionMismatchException if the array is not valid<a name="line.581"></a>
<FONT color="green">582</FONT>         * @throws NotPositiveException if the array contains any negative entries<a name="line.582"></a>
<FONT color="green">583</FONT>         */<a name="line.583"></a>
<FONT color="green">584</FONT>        private void checkArray(final long[][] in)<a name="line.584"></a>
<FONT color="green">585</FONT>            throws NullArgumentException, DimensionMismatchException,<a name="line.585"></a>
<FONT color="green">586</FONT>            NotPositiveException {<a name="line.586"></a>
<FONT color="green">587</FONT>    <a name="line.587"></a>
<FONT color="green">588</FONT>            if (in.length &lt; 2) {<a name="line.588"></a>
<FONT color="green">589</FONT>                throw new DimensionMismatchException(in.length, 2);<a name="line.589"></a>
<FONT color="green">590</FONT>            }<a name="line.590"></a>
<FONT color="green">591</FONT>    <a name="line.591"></a>
<FONT color="green">592</FONT>            if (in[0].length &lt; 2) {<a name="line.592"></a>
<FONT color="green">593</FONT>                throw new DimensionMismatchException(in[0].length, 2);<a name="line.593"></a>
<FONT color="green">594</FONT>            }<a name="line.594"></a>
<FONT color="green">595</FONT>    <a name="line.595"></a>
<FONT color="green">596</FONT>            MathArrays.checkRectangular(in);<a name="line.596"></a>
<FONT color="green">597</FONT>            MathArrays.checkNonNegative(in);<a name="line.597"></a>
<FONT color="green">598</FONT>    <a name="line.598"></a>
<FONT color="green">599</FONT>        }<a name="line.599"></a>
<FONT color="green">600</FONT>    <a name="line.600"></a>
<FONT color="green">601</FONT>    }<a name="line.601"></a>




























































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